if `0ltalphaltbetaltgammaltpi/ 2,`then prove that `tanalpha lt (sinalpha+sinbeta+singamma)/ (cosalpha+cosbeta+cosgamma)lt tangamma`

If alpha+beta+gamma=pi , prove that : cos^2 alpha + cos^2 beta + cos^2 gamma+2cosalpha cosbeta cosgamma=1 .

If 0ltalphaltbetaltpi/2, show that (sinalpha)/alphagt(sinbeta)/beta

sinalpha+sinbeta=a ,cosalpha+cosbeta=b=>sin(alpha+beta)

If alpha,beta,gamma, in (0,pi/2) , then prove that (s i(alpha+beta+gamma))/(sinalpha+sinbeta+singamma)<1

If cosalpha+cosbeta+cosgamma=0 , then prove that cos3alpha+cos3beta+cos3gamma=12cosalphacosbetacosgamma

If 0 lt alpha lt (pi)/(3) , then prove that alpha (sec alpha) lt (2pi)/(3).

If 0 lt alpha lt pi/2 then show that tanalpha+cotalphagtsinalpha+cosalpha

If sinalpha+sinbeta=a ,cosalpha+cosbeta=b=>sin(alpha+beta) =

If 0ltalphaltbetaltgammaltpi/2 then the equation 1/(x-sinalpha)+1/(x-sinbeta)+1/(x-singamma)=0 has (A) imaginary roots (B) real and equal roots (C) real and unequal roots (D) rational roots

If 0 lt alpha lt beta lt gamma lt pi//2 , then the equation (x-sinbeta)(x-singamma)+(x-sinalpha)(x-singamma)+(x-sinalpha)(x-sinbeta)=0 has